Find the length of the curve. r(t)=\langle6t,\ t^{2},\ \frac{1}{9}t^{3}\rangle,\ 0\leq t\leq1

tabita57i

tabita57i

Answered question

2021-06-06

Find the length of the curve.
r(t)=6t, t2, 19t3, 0t1

Answer & Explanation

cyhuddwyr9

cyhuddwyr9

Skilled2021-06-07Added 90 answers

Step 1
r(t)=6t, t2, t39r(t)=6, 2t, t23
|r(t)|=36+4t2+t49
=13t4+36t2+324
=13(t2+18)2+t2+183
Length of the curve: L=01|r¯(t)|dt=0113(t2+18)dt
=01(t23+b)dt
=[t39+bt]01
=19+b0=19+6=559

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